Do you know what the rated voltage/current is for those motors? If the motors want to draw more than 1.5A (together) then clearly the power supply is not sufficient.
You are right that voltage must be proper for the motors, and current must be greater than the sum of the current demands of all loads (motors in this case.) Additionally, you MAY want to look at things like transient step response. Ir just add a big capacitor and call it good :-)
Three other properties that matter for power supplies are:
- Output voltage ripple. Not so important for motors; very important for logic.
- Overcurrent protection mode. If it's "hiccup mode" then the power supply may stop delivering power when a large load is connected, and then come back, repeat. I prefer "constant current limiting" mode that drops the voltage until the current is properly controlled.
- Efficiency. A 75% efficient power supply will generate a LOT more heat than a 95% efficient power supply.
My guess, from the vague data available, is that your power supply is "hiccup mode" protected, and that your motor or motors draw more than 1.5A together, at least temporarily (say, when starting up.)
Reading the specifications for the motors, and measuring things with an oscilloscope and multimeter, would be the next step in trying to define the problem.